We do have an extremely good understanding of how gravity causes stellar fusion. We don't need quantum gravity to model that. The gravitationally-induced pressure due to the star’s total mass provide the conditions needed for fusion.
If you're thinking along the lines that if we knew how gravity worked at the quantum scale, we might find some sort of way to achieve fusion under much less extreme conditions, we probably can't entirely rule that out, but there's been many decades of work in that area, so it's seeming pretty unlikely. Also, that has nothing to do with what's happening inside a star.
We know about the need to overcome the electrostatic Coulomb barrier, we know what energies are required to overcome it and have models that predict those energies very accurately, we know how quantum tunneling allows this barrier to be penetrated, etc.
We can even do things like muon-catalyzed fusion, where we substitute muons for electrons in hydrogen atoms, which lowers the Coulomb barrier.
As such, the claims in the comment I originally replied to were just completely wrong.
If you're thinking along the lines that if we knew how gravity worked at the quantum scale, we might find some sort of way to achieve fusion under much less extreme conditions, we probably can't entirely rule that out, but there's been many decades of work in that area, so it's seeming pretty unlikely. Also, that has nothing to do with what's happening inside a star.
We know about the need to overcome the electrostatic Coulomb barrier, we know what energies are required to overcome it and have models that predict those energies very accurately, we know how quantum tunneling allows this barrier to be penetrated, etc.
We can even do things like muon-catalyzed fusion, where we substitute muons for electrons in hydrogen atoms, which lowers the Coulomb barrier.
As such, the claims in the comment I originally replied to were just completely wrong.